Re: Simplify for ca^2+sa^2==1

• To: mathgroup at smc.vnet.net
• Subject: [mg26370] Re: [mg26339] Simplify for ca^2+sa^2==1
• From: BobHanlon at aol.com
• Date: Wed, 13 Dec 2000 02:41:28 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```If you are using version 4:

((1 + ca^2 + sa^2)(b + 3 + 5ca^2 + 5sa^2))/((4 - ca^2 - sa^2)(x - 3y + ca^2 +
sa^2));

Simplify[%, (ca^2 + sa^2) == 1]

(2*(8 + b))/(3*(1 + x - 3*y))

Bob Hanlon

In a message dated 12/12/00 3:35:54 AM, hanssen at Zeiss.de writes:

>in a lengthy expression, I know, a lot
>of simplification can be done, if Simplify
>and the like would take into account that
>for varaibles ca and sa
>
>ca^2+sa^2==1
>
>I know, that I can set ca=Sqrt[1-sa^2] and
>deal with the branch cut by hand.
>
>The bad thing is, that these ca^2 and sa^2
>are expanded out in lenghty subexpressions
>involving lots of other symbols. So far, I
>have found no way (but would be glad, if
>someone could advise me one), to factor out
>(ca^2+sa^2).
>
>Unfortunately, there are also terms, where
>(1+ca^2+sa^2) or (2*ca^2+2*sa^2) can be
>factored out, also others with (-ca^2-sa^2)
>and so on.
>
>Any general tip, how to best cope with such
>algebraic manipulations?
>

```

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